## Taiwanese Journal of Mathematics

### Maximal Regularity for Integral Equations in Banach Spaces

Shangquan Bu

#### Abstract

We study maximal regularity in periodic Besov spaces $B_{p,q}^s(\mathbb T, X)$ for the integral equations ($P$): $u(t) = A \int^{t}_{-\infty} a(t-s) u(s) ds) + B \int^{t}_{-\infty} b(t-s) u(s) ds + f(t)$ on $[0,2\pi]$ with periodic boundary condition $u(0) = u(2\pi)$, where $A$ and $B$ are closed operators in a Banach space $X$, $a, \ b \in L^1(\mathbb R_+)$ and $f$ is a given function defined on $[0,2\pi]$ with values in $X$. Under suitable assumptions on the kernels $a, \ b$ and the closed operators $A, \ B$, we completely characterize $B_{p,q}^s$-maximal regularity of ($P$).

#### Article information

Source
Taiwanese J. Math., Volume 15, Number 1 (2011), 229-240.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500406172

Digital Object Identifier
doi:10.11650/twjm/1500406172

Mathematical Reviews number (MathSciNet)
MR2780282

Zentralblatt MATH identifier
1245.45009

#### Citation

Bu, Shangquan. Maximal Regularity for Integral Equations in Banach Spaces. Taiwanese J. Math. 15 (2011), no. 1, 229--240. doi:10.11650/twjm/1500406172. https://projecteuclid.org/euclid.twjm/1500406172

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